Good point. It is of course magic and entirely theoretical, but even in a magical scenario, I think there would need to be some way of determining who is theoretically capable of the choice, and a default result for refusal to choose at all or to push both buttons at once. Any attempt to figure out the default would require a calculation of how many people would decline the challenge, since if enough people can be expected to do so, the default will occur automatically.
I can't think of a fair way this could be done in an actual real world.
While we're at it, thinking about this also brings about an interesting complication I don't think has been covered much here. If the vote and result exclude both children and the incompetent, any outcome that has red prevailing will leave the remaining population disproportionately responsible not only for an indeterminately large number of newly orphaned children, right down to nursing newborns whose parents suddenly vanish before their eyes, but all those who are mentally handicapped or insane. I would expect the prospect of this might also influence the choice. If there is a post-red apocalypse the survivors will pay a high price, and the ethical choice that led them there will be only the first of more to come.